简介:Theproblemofwaterwavescatteringbyathinverticalelasticplatesubmergedinuniformfinitedepthwaterisinvestigatedhere.TheboundaryconditionontheelasticplateisderivedfromtheBernoulli-Eulerequationofmotionsatisfiedbytheplate.UsingtheGreen’sfunctiontechnique,fromthisboundarycondition,thenormalvelocityoftheplateisexpressedintermsofthedifferencebetweenthevelocitypotentials(unknown)acrosstheplate.Thetwoendsoftheplateareeitherclampedorfree.Thereflectionandtransmissioncoefficientsareobtainedintermsoftheintegrals’involvingcombinationsoftheunknownvelocitypotentialonthetwosidesoftheplate,whichsatisfythreesimultaneousintegralequationsandaresolvednumerically.Thesecoefficientsarecomputednumericallyforvariousvaluesofdifferentparametersanddepictedgraphicallyagainstthewavenumberinanumberoffigures.
简介:Thescatteringprobleminvolvingwaterwavesbysmallundulationontheporousocean-bedinatwo-layerfluid,isinvestigatedwithintheframeworkofthetwo-dimensionallinearwaterwavetheorywheretheupperlayeriscoveredbyathinuniformsheetoficemodeledasathinelasticplate.Insuchatwo-layerfluidthereexistwaveswithtwodifferentmodes,onewithalowerwavenumberpropagatealongtheice-coverwhilstthosewithahigherwavenumberpropagatealongtheinterface.Anincidentwaveofaparticularwavenumbergetsreflectedandtransmittedoverthebottomundulationintowavesofbothmodes.PerturbationanalysisinconjunctionwiththeFouriertransformtechniqueisusedtoderivethefirst-ordercorrectionsofreflectionandtransmissioncoefficientsforboththemodesduetoincidentwavesoftwodifferentmodes.Onespecialtypeofbottomtopographyisconsideredasanexampletoevaluatetherelatedcoefficientsindetail.Thesecoefficientsaredepictedingraphicalformstodemonstratethetransformationofwaveenergybetweenthetwomodesandalsotoillustratetheeffectsoftheicesheetandtheporosityoftheundulatingbed.